The assault got under way this evening after sustained U.S. air strikes and a continuous artillery barrage.

News correspondents reported that some 4,000 U.S. Marines, backed by tanks and other armored vehicles, began fighting their way into the city center from positions on the outskirts.

Defense Secretary Donald Rumsfeld later described "coordinated offensive operations" by coalition and Iraqi forces "to restore law and order" in and around the city. Rumsfeld added that the conflict is necessary to ensure Iraq's future as a "free, and a peaceful, society."

Allawi said today that the offensive is aimed at rooting out terrorists and establishing the rule of law in Al-Fallujah, 50 kilometers west of Baghdad. He also said he had imposed a curfew on Al-Fallujah and nearby Ramadi.

"I have given my authority to the multinational forces, I have given my authority to the Iraqi forces to spearhead the multinational forces with help. We are determined to clean Fallujah from terrorists. The curfew is intended to protect whoever remained from the Fallujah people, the decent people of Fallujah," Allawi said.

Allawi said 38 rebels were killed as the U.S. military seized control of a hospital and two bridges in Al-Fallujah early today. Most of the city's residents have fled.